Evaluate (5/8)^2-(1/4-1/20)÷(8/5)

${(\frac{5}{8})}^{2} - (\frac{1}{4} - \frac{1}{20}) \div \frac{8}{5}$

Step 1

Simplify each term.

Apply the product rule to $\frac{5}{8}$ .

$\frac{5^{2}}{8^{2}} - (\frac{1}{4} - \frac{1}{20}) \div \frac{8}{5}$

Raise $5$ to the power of $2$ .

$\frac{25}{8^{2}} - (\frac{1}{4} - \frac{1}{20}) \div \frac{8}{5}$

Raise $8$ to the power of $2$ .

$\frac{25}{64} - (\frac{1}{4} - \frac{1}{20}) \div \frac{8}{5}$

To divide by a fraction, multiply by its reciprocal.

$\frac{25}{64} - ((\frac{1}{4} - \frac{1}{20}) \frac{5}{8})$

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{25}{64} - ((\frac{1}{4} \cdot \frac{5}{5} - \frac{1}{20}) \frac{5}{8})$

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{4}$ by $\frac{5}{5}$ .

$\frac{25}{64} - ((\frac{5}{4 \cdot 5} - \frac{1}{20}) \frac{5}{8})$

Multiply $4$ by $5$ .

$\frac{25}{64} - ((\frac{5}{20} - \frac{1}{20}) \frac{5}{8})$

Combine the numerators over the common denominator.

$\frac{25}{64} - (\frac{5 - 1}{20} \cdot \frac{5}{8})$

Subtract $1$ from $5$ .

$\frac{25}{64} - (\frac{4}{20} \cdot \frac{5}{8})$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$\frac{25}{64} - (\frac{4}{20} \cdot \frac{5}{4 (2)})$

Cancel the common factor.

$\frac{25}{64} - (\frac{4}{20} \cdot \frac{5}{4 \cdot 2})$

Rewrite the expression.

$\frac{25}{64} - (\frac{1}{20} \cdot \frac{5}{2})$

Cancel the common factor of $5$ .

Factor $5$ out of $20$ .

$\frac{25}{64} - (\frac{1}{5 (4)} \cdot \frac{5}{2})$

Cancel the common factor.

$\frac{25}{64} - (\frac{1}{5 \cdot 4} \cdot \frac{5}{2})$

Rewrite the expression.

$\frac{25}{64} - (\frac{1}{4} \cdot \frac{1}{2})$

Multiply $\frac{1}{4}$ by $\frac{1}{2}$ .

$\frac{25}{64} - \frac{1}{4 \cdot 2}$

Multiply $4$ by $2$ .

$\frac{25}{64} - \frac{1}{8}$

Step 2

To write $- \frac{1}{8}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{25}{64} - \frac{1}{8} \cdot \frac{8}{8}$

Step 3

Write each expression with a common denominator of $64$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{8}$ by $\frac{8}{8}$ .

$\frac{25}{64} - \frac{8}{8 \cdot 8}$

Multiply $8$ by $8$ .

$\frac{25}{64} - \frac{8}{64}$

Step 4

Combine the numerators over the common denominator.

$\frac{25 - 8}{64}$

Step 5

Subtract $8$ from $25$ .

$\frac{17}{64}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{64}$

Decimal Form:

$0.265625$

Evaluate (5/8)^2-(1/4-1/20)÷(8/5)

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